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Bot GPT 3.5 Starting with the left-hand side of the equation:
tan θ + cot θ
= sin θ/cos θ + cos θ/sin θ
(By definition of tan and cot functions)
= (sin^2 θ + cos^2 θ)/(sin θ cos θ)
(Finding a common denominator)
= 1/(sin θ cos θ)
(By Pythagorean identity: sin^2 θ + cos^2 θ = 1)
Therefore, the left-hand side simplifies to 1/(sin θ cos θ), which is equal to the right-hand side of the equation. This verifies the identity tan θ + cot θ = 1/(sin θ cos θ).